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generalized pattern search methods for a class of nonsmooth optimization problems with structure

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期229卷 283-293页

作者： Bogani, C. Gasparo, M. G. Papini, A. Univ Florence Dip Energet S Stecco I-50134 Florence Italy Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England

We propose a generalized pattern search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method. (C) 2008 Elsevier B.V. All rights reserved.

关键词： generalized pattern search Nonsmooth optimization Linear constraints Clarke's differential calculus

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generalized pattern search methods for linearly equality constrained optimization problems

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期181卷 527-535页

作者： Liu, LiYing Zhang, XueSheng Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China

Torczon and several persons have designed pattern search methods for unconstrained optimization problem, bound constrained, and linearly constrained optimization problems. In this paper, we shall consider linear equality constrained problems as unconstrained ones using generalized pattern search algorithm, except for a feasible starting point. (c) 2006 Elsevier Inc. All rights reserved.

关键词： generalized pattern search linear equality constraint convergence optimization positive bases positive spanning set

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generalized pattern search for Solving Materials Properties Determination Inverse Problem

Generalized Pattern Search for Solving Materials Properties ...

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International Symposium on Electromagnetic Fields in Electrical Engineering (ISEF)

作者： Mohdeb, Naamane Mekideche, Mohamed Rachid Hacib, Tarik Belli, Zoubida Bouchekhou, Hocine Chebout, Mohamed Jijel Univ Dept Elect Engn LAMEL Lab Ouled Aissa Algeria

ISBN: (纸本)9781607506041;9781607506034

A generalized pattern search method is applied to forecast the ferromagnetic properties of a material under test. A GPS is used as the new method in electrical engineering for complete the parameters identification problem or solving materials properties determination inverse problem. Both the coupled electromagnetic circuits method (CECM) and the new approach (GPS) are used to estimate the electric conductivity and magnetic permeability of a circular material under test.

关键词： Coupled Electromagnetic Circuits Method generalized pattern search Parameters Identification Inverse Problem

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Precision control for generalized pattern search algorithms with adaptive precision function evaluations

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SIAM JOURNAL ON OPTIMIZATION 2006年第3期16卷 650-669页

作者： Polak, E Wetter, M Univ Calif Berkeley Dept Elect Engn Berkeley CA 94720 USA United Technol Res Ctr E Hartford CT 06108 USA

In the literature on generalized pattern search algorithms, convergence to a stationary point of a once continuously differentiable cost function is established under the assumption that the cost function can be evaluated exactly. However, there is a large class of engineering problems where the numerical evaluation of the cost function involves the solution of systems of differential algebraic equations. Since the termination criteria of the numerical solvers often depend on the design parameters, computer code for solving these systems usually defines a numerical approximation to the cost function that is discontinuous with respect to the design parameters. Standard generalized pattern search algorithms have been applied heuristically to such problems, but no convergence properties have been stated. In this paper we extend a class of generalized pattern search algorithms to include a subprocedure that adaptively controls the precision of the approximating cost functions. The numerical approximations to the cost function need not de. ne a continuous function. Our algorithms can be used for solving linearly constrained problems with cost functions that are at least locally Lipschitz continuous. Assuming that the cost function is smooth, we prove that our algorithms converge to a stationary point. Under the weaker assumption that the cost function is only locally Lipschitz continuous, we show that our algorithms converge to points at which the Clarke generalized directional derivatives are nonnegative in predefined directions. An important feature of our adaptive precision scheme is the use of coarse approximations in the early iterations, with the approximation precision controlled by a test. We show by numerical experiments that such an approach leads to substantial time savings in minimizing computationally expensive functions.

关键词： algorithm implementation approximations generalized pattern search Hooke Jeeves Clarke's generalized directional derivative nonsmooth optimization

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Endmembers abundance estimators based on spectral shape similarity using genetic algorithm and generalized pattern search algorithm

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JOURNAL OF APPLIED REMOTE SENSING 2019年第2期13卷

作者： Moness, Mohammed Massoud, Mohammed A. Kaldas, Marco Mourad Menia Univ Fac Engn Comp & Syst Dept Al Minya Egypt Menia Univ Fac Engn Biomed Dept Al Minya Egypt

We develop two endmembers abundance estimators based on a genetic algorithm (GA) and a generalized pattern search algorithm. This development aims to estimate more accurate abundances of endmembers in cases of brightness and shading noises, which is an issue in other endmember abundance estimation methods based on the least square method, such that the estimators depend on spectral shape similarity as a matching criterion between spectral signatures, because shape similarity methods are independent on the spectral reflectance amplitude and not sensitive to brightness noise effects on it. The strategy used for unmixing problem analysis is based on the popular linear spectral mixture model. GA is used as a heuristic optimization technique, and generalized pattern search is used as a direct search algorithm. Spectral angle mapper, spectral information divergence methods, and the combination of both of these are used as objective functions for optimization techniques. All experiments have been performed on the proposed estimators and the traditional fully constrained least squares method as a state-of-theart method. Experiments have been applied on simulated multispectral and hyperspectral datasets with different noise conditions. In addition, a hyperspectral real dataset from a cuprite region (Las Vegas, Nevada, USA) was used for testing performance. The experimental results show that proposed estimators are better than fully contained least squares method across all experiments and especially in cases of noisy datasets. (C) 2019 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： hyperspectral unmixing endmembers abundances estimation generalized pattern search genetic algorithm spectral shape similarity

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Adaptive System Protection Scheme using generalized pattern search 18

Adaptive System Protection Scheme using Generalized Pattern ...

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2015 18th International Conference on Intelligent System Application to Power Systems (ISAP)

作者： Lopez, Javier Hsiao, Yang-Che Hsiao, Tsun-Yu Lu, Chan-Nan

ISBN: (纸本)9781509001910

Due to physical limitations of power network and ever growing power demands from customers, utilities are facing the challenge of providing a high quality and continuous electricity supply. In order to maintain the stability of the network, increasing the infrastructure capacity becomes necessary. Alternatively, utilities can implement SPS (System Protection Schemes) as a short-term cost-effective solution. SPS are custom tailored schemes dealing with specific events to prevent system deterioration. SPS are usually designed for predefined conditions and their respective pre-calculated actions are based upon the worst case scenario. This paper proposes an intelligent SPS design scheme that adapts to different load scenarios by using state estimation results to update the necessary control actions to prevent the network from collapse due to loss of synchronism. The study results indicate that the proposed algorithm can prevent angular instability and enhance network reliability. The continuous update scheme proposed can optimize the controls required in a time frame for fast actions to prevent system instability.

关键词： System Protection Schemes generalized pattern search Intelligent System

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Optimization of a tuned liquid column damper subject to an arbitrary stochastic wind

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2018年第11期40卷 1-11页

作者： Alkmim, Mansour H. Fabro, Adriano T. de Morais, Marcus V. G. Univ Brasilia Dept Mech Engn BR-70910900 Brasilia DF Brazil

The current Brazilian energy scenario is undergoing impactful changes. There is a clear need to adjust the current energy sector that presents an imbalance due to the almost exclusively dependency on hydroelectric power. This brings the need of diversifying the Brazilian energy matrix, including other energy sources that are both efficient and renewable. Amongst the available options, the wind energy stands out. Remarkable progress in wind turbine technology has been made over the past years, allowing the design of higher and slender structures for increasing efficiency in energy production. Parameter optimization for tuned liquid column dampers (TLCD), a class of passive structural control, has been previously proposed in the literature for reducing vibration in wind turbines and several other applications. However, most of the available work considers the wind excitation as either a deterministic harmonic load or random load with white noise spectra, which might not be representative of the actual wind load. This paper proposes an optimization approach for the TLCD parameters subjected to an arbitrary wind spectrum, given that its power spectral density is know. Finally, a numerical example is given in which a simplified wind turbine model is loaded by different stochastic wind profiles. Satisfactory reduction in the response vibration levels is found, and it is shown that different wind profiles can significantly affect the optimization results, i.e. the best TLCD parameters are dependent on the wind model.

关键词： Vibration suppression Parameter optimization generalized pattern search Random vibration analysis TLCD

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BuildOpt - a new building energy simulation program that is built on smooth models

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BUILDING AND ENVIRONMENT 2005年第8期40卷 1085-1092页

作者： Wetter, M Lawrence Berkeley Lab Bldg Technol Dept Environm Energy Technol Div Simulat Res Grp Berkeley CA 94720 USA

Building energy simulation programs compute numerical approximations to physical phenomena that can be modeled by a system of differential algebraic equations (DAE). For a large class of building energy analysis problems, one can prove that the DAE system has unique solution that is once continuously differentiable in the building design parameters. Consequently, if building simulation programs are built on models that satisfy the smoothness assumptions required to prove existence of a unique smooth solution, and if their numerical solvers allow controlling the approximation error, one can use such programs with generalized pattern search optimization algorithms that adaptively control the precision of the solutions of the DAE system. Those optimization algorithms construct sequences of iterates with stationary accumulation points and have been shown to yield a significant reduction in computation time compared to algorithms that use fixed precision cost function evaluations. In this paper, we state the required smoothness assumptions and present the theorems that state existence of a unique smooth solution of the DAE system. We present BuildOpt, a detailed thermal and daylighting building energy simulation program. We discuss examples that explain the smoothing techniques used in BuildOpt. We present numerical experiments that compare the computation time for an annual simulation with the smoothing techniques applied to different parts of the models. The experiments show that high precision approximate solutions can only be computed if smooth models are used. This is significant because today's building simulation programs do not use such smoothing techniques and their solvers frequently fail to obtain a numerical solution if the solver tolerances are tight. We also present how BuildOpt's approximate solutions converge to a smooth function as the precision parameter of the numerical solver is tightened. (c) 2004 Published by Elsevier Ltd.

关键词： building energy simulation adaptive precision simulation differential algebraic equations optimization generalized pattern search

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Investigation of a Voronoi Diagram Representation for the Computational Design of Additively Manufactured Discrete Lattice Structures

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JOURNAL OF MECHANICAL DESIGN 2020年第11期142卷 111704页

作者： Stankovic, Tino Shea, Kristina Swiss Fed Inst Technol Zurich ETHZ Dept Mech & Proc Engn Engn Design & Comp Lab EDAC Tannenstr 3 CH-8092 Zurich Switzerland

A lattice structure is defined by a network of interconnected structural members whose architecture exhibits some degree of regularity. Although the overall architecture of a lattice may contain many members, its generation can be a simple process in which a unit cell composed of a small amount of members, in comparison to the overall structure, is mapped throughout the Euclidean space. However, finding the right lattice architecture in a vast search space that customizes the behavior of a design for a given purpose, subject to mechanical and manufacturing constraints, is a challenging task. In response to this challenge, this work investigates a Voronoi diagram-based tessellation of a body-centered cubic cell for applications in structural synthesis and computational design of 3D lattice structures. This work contributes by exploring how the Voronoi tessellation can be utilized to parametrically represent the architecture of a lattice structure and what the implications of the parametrization are on the optimization, for which a global direct search method is used. The work considers two benchmark studies, a cubic and a cantilever lattice structure, as well as the effect of isotropic and anisotropic material property models, stemming from applications to additive manufacturing. The results show that the proposed parameterization generates complex search spaces using only four variables and includes four different lattice structure types, a Kelvin cell, a hexagonal lattice, a diamond-core lattice structure, and a box-boom type lattice structure. The global direct search method applied is shown to be effective considering two different material property models from an additive manufacturing (AM) process.

关键词： lattice structures Voronoi diagram discrete structural optimization generalized pattern search additive manufacturing computational geometry design optimization design representation

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Multi-fidelity algorithms for the horizontal alignment problem in road design

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ENGINEERING OPTIMIZATION 2020年第11期52卷 1848-1867页

作者： Aziz, Mahdi Hare, Warren Jaberipour, Majid Lucet, Yves Univ British Columbia Irving K Barber Sch Arts & Sci Comp Sci Math Phys Comp Sci Kelowna BC Canada Univ British Columbia Math IKBSAS CMPS Kelowna BC Canada

Multi-fidelity algorithms for solving the horizontal alignment problem in road design are considered. A multi-fidelity surrogate model is built and quantile regression is used to understand its accuracy at various fidelity levels. Two algorithms are compared: a generalized pattern search algorithm with adaptive precision control, and a trust-region algorithm for unconstrained problems with controlled error. To make a fair comparison, the parameters of each algorithm are tuned on five small roads using performance profiles. Then the algorithms are evaluated on 35 roads, ranging from small to very large roads. The results show that using multi-fidelity surrogates in optimization algorithms provide notable speed-up when compared to single-fidelity algorithms while preserving the quality of solutions (cost error ). On the longest roads, higher speed-up and better accuracy are observed.

关键词： Multi-fidelity road design surrogate generalized pattern search trust region

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